Field
The present application relates to analysis of immiscible or partially miscible fluids. Specifically, the present application relates to measuring the interfacial tension between immiscible or partially miscible fluids.
Related Art
A fluid is a substance that continually deforms or flows under an applied shear stress. It may contain liquids, gases, and solids, and generally takes on the shape of the container in which it is housed.
An emulsion is a fluid that consists of a mixture of at least two fluid phases that are immiscible or partially miscible with respect to one another. In a two-phase emulsion, one fluid (the dispersed phase) is dispersed within the other (the continuous phase). The creation of an emulsion from separate phases typically requires stirring, shaking, or some other form of energy input. The process by which emulsions are created is called emulsification. In an emulsion, the degree and uniformity of dispersion of the dispersed phase within the continuous phase will generally depend on the nature of the fluid phases of the emulsion, the rate of mixing, and the length of time that the fluid phases are mixed. If the interfacial tension between the dispersed and continuous phases of an emulsion is low or the kinetic stability of the thin liquid films between the approaching emulsion droplets is low, then the emulsion could be unstable. Over time, the components of an unstable emulsion tend to separate if the mixing, stirring, or shaking is ceased. One common example of an emulsion that quickly separates is oil and vinegar salad dressing. When an oil and vinegar salad dressing bottle is shaken, the components of the salad dressing are temporarily dispersed. When the shaking ceases, the components separate.
Because the molecules at the surface of a liquid have potential energies greater than those of similar molecules in the interior of the liquid, an amount of work equal to this difference in potential energy must be expended to bring a molecule from the interior to the surface. Surface tension is proportional to this work. At the interface between the dispersed and continuous phases of an emulsion, the dissimilar molecules in the adjacent layers facing each other across the interface also have potential energies different from those in their respective phases. Each molecule at the interface has a potential energy greater than that of a similar molecule in the interior of its bulk phase by an amount equal to its interaction energy with the bulk phase across the interface. For most purposes, however, only interactions with adjacent molecules need to be taken into account. Because of the differences in potential energies for the molecules of the interface, work must be expended to form the interface. Interfacial tension is a measure of such work.
Interfacial tension is an important parameter in reservoir engineering calculations. For example, it is often used to determine capillary number in a reservoir. Capillary number is a dimensionless parameter that characterizes the ratio of viscous forces to interfacial tension forces. For a flowing liquid, if the capillary number is much greater than 1, then viscous forces dominate over interfacial forces; however if the capillary number is much less than 1, then viscous forces are negligible compared with interfacial forces. Interfacial tension is also used to derive capillary pressure and saturation profiles in a reservoir.
Interfacial tension is also a basic parameter that can be used to study the stability of emulsions, efficiency of cleaning and washing operations, and the properties of surfactants. A surfactant reduces the interfacial tension by adsorbing at the interface between the dispersed and continuous phases of the emulsion. In enhanced oil recovery applications, such as water flooding, steam flooding, or steam assisted gravity drainage (SAGD), high interfacial tension at the oil-water interface can prevent the migration of oil in the reservoir and thus hinder production. The surfactant is injected into the reservoir in conjunction with the water or steam in order to reduce the interfacial tension at the oil-water interface and thus improve the migration of oil in the reservoir and aid in production of the reservoir. When planning such enhanced oil recovery operations, a large number of surfactants are screened to characterize the interfacial tension at the temperature and pressure conditions of the reservoir.
Interfacial tension between the dispersed phase and the continuous phase of an emulsion can be measured with the interface in a state of full thermodynamic equilibrium. This is typically referred to as static interfacial tension. Full thermodynamic equilibrium requires thermodynamic equilibrium between the bulk of the phases of the emulsion and the interface, in addition to the usually understood equilibrium conditions for the bulk of the phases. The interface itself should also be in equilibrium, which means, among other things, that the lifetime of interface should approach infinity.
Interfacial tension between the dispersed phase and continuous phase of an emulsion can be measured with the interface not in a state of full thermodynamic equilibrium. This is typically referred to as dynamic interfacial tension. Measurements of dynamic interfacial tension can be made on non-equilibrated interfaces, which are generated by either interfacial area expansion or reduction. The interfacial area generation is more often used in practice. For this case, the new interface can be generated in a single step and the interfacial tension will be time dependent. It is also possible to generate new interfaces continuously. In this case, the interfacial tension will be location dependent. Generally, the dynamic interfacial tension is dependent on the lifetime of the interface studied and its value approaches the static interfacial tension asymptotically in time.
There are a number of known methodologies for measuring interfacial tension. For example the capillary rise, sessile drop, spinning drop, and maximum bubble pressure methodologies are often used and commercial instruments are usually available employing these specific methodologies. The densities of the phases are most often needed to measure the interfacial tension. For measuring dynamic interfacial tension, the densities of the phases can change significantly during the equilibration process. Using the densities for the phases assuming static conditions can lead to errors in measuring dynamic interfacial tension. See Mahavadi, C. S., Zacharia, J., and Horvath-Szabo, G., “The Impact of Pre-equilibration on the Assessment Methodology of Interfacial Tension Measured between Aqueous and Heavy Oil Phases,” Energy & Fuels, 25(6), 2011, pp. 2542-2550.
In biology, the micropipette methodology is often used to measure the tension of cell membranes. This approach is based on capturing a single cell with a pipette having an orifice diameter smaller than the diameter of the cell. A small suction pressure is applied in the pipette to keep the cell at the top of the pipette for capturing. To measure the membrane tension, the suction pressure is smoothly increased until a portion of the cell is drawn into the capillary while the rest of the cell remains outside. At this stage, the suction pressure applied on the capillary is counterbalanced by the Laplace pressure differences of the curvatures of the two spherical segments of membrane, which are inside and outside of the capillary. Because the Laplace pressure is dependent on the radius of the curvature and the membrane tension, the membrane tension can be obtained by simple algebraic manipulations using the curvatures of the two spherical segments and the suction pressure.
The applicability of the micropipette methodology for oil-water systems was demonstrated by comparing the interfacial tension of different hydrocarbon/water systems measured by some traditional technique and the micropipette method. See Yeung, A., Dabros, T., Masliyah, J., and Czarnecki, J., “Micropipette: a new technique in emulsion research,” Colloids and Surfaces, A: Physicochemical and Engineering Aspects, Volume 174, Issues 1-2, 15 Nov. 2000, pp. 169-181. For measuring the interfacial tension of a given hydrocarbon-water system, suction pressure was applied to a micropipette to capture a single emulsion droplet at the entrance to an interior capillary chamber of the micropipette. The interior capillary chamber was either hydrophobic (i.e., zero contact angle could be assumed for an oil phase droplet where oil-in-water emulsions were studied) or hydrophilic (i.e., zero contact angle could be assumed for an aqueous phase droplet where water-in-oil emulsions were studied). After capturing the droplet at the entrance to the interior capillary chamber, the suction pressure was gradually increased, which causes the radius of curvature of the oil-water interface within the interior capillary chamber to become smaller. There is a range of suction pressure within which the droplet stays attached at the entrance of the interior capillary chamber. When the radius of curvature of the interface situated inside the interior capillary chamber becomes equal to the internal radius of the interior capillary chamber, the suction pressure reaches its maximal or critical value, pcr. When the pressure is increased beyond the critical value pcr, the emulsion droplet is completely sucked into the interior capillary chamber. The methodology measured the interfacial tension (σ) of the given hydrocarbon-water system with the following formula:
                    σ        =                                            p              cr                        ⁢                          R              p                                            2            ⁢                          (                              1                -                                                      R                    p                                    /                                      R                    o                                                              )                                                          (        1        )                            where pcr is the critical suction pressure,        Rp is the radius of the interior capillary chamber, and        Ro is the radius of the drop segment that lies outside the interior capillary chamber.These radii were obtained from image analysis, while the suction pressure was measured by a sensor. The above-described methodology has some disadvantages. First, it requires human intervention for capturing the droplet. Second, it requires simultaneous usage of inverted microscopy, micromanipulators, and a suction pump to capture individual emulsion droplets. Third, it requires a means for measuring the critical pressure by slowly increasing the suction pressure while observing the droplet under the microscope. Fourth, it requires image analysis to measure the radius of the interior capillary chamber and/or the radius of the droplet segment that lies outside the interior capillary chamber, and the internal capillary radius. Fifth, the droplet capture and image analysis operations require manual intervention with well-trained personnel. Sixth, the droplet capture and image analysis operations are not suited for high temperature and pressure conditions.        
Another method of measuring interfacial tension using a micropipette has been described in Lee, S., Kim, D. H., and Needham, D., “Equilibrium and Dynamic Interfacial Tension Measurements at Microscopic Interfaces Using a Micropipet Technique. 1. A New Method for Determination of Interfacial Tension,” Langmuir 2001, 17(18), pp. 5537-5543. In this method, the meniscus of the interface of a two-phase system is optically observed in a taped micropipette, and the radius of curvature of the meniscus of the interface is measured together with the pressure necessary to maintain the interface at the same position. From the pressure and the curvature, the interfacial tension (γ) can be calculated by the Laplace equation as follows:
                    γ        =                              R            ⁢                                                  ⁢            1            ⁢                                                  ⁢            Δ            ⁢                                                  ⁢            P            ⁢                                                  ⁢            1                    2                                    (        2        )                            where R1 is the radius of curvature of the meniscus of the interface geometry, and        ΔP1 is the pressure necessary to maintain the interface in equilibrium.The radius of curvature of the meniscus can measured at different pressures. The slope of the pressure versus radius of curvature curve can be used to determine the interfacial tension (γ) with higher precision because of the multiple data points. The above-described methodology has some disadvantages. First, it requires human intervention for capturing the interface and maintaining it in a stationary position within the micropipette. Second, it requires a means for measuring the pressure ΔP1 with the interface maintained in the stationary position within the micropipette. Third, it requires image analysis to measure the radius of curvature of the meniscus while the interface is maintained in the stationary position within the micropipette. Fourth, the measurement and image analysis operations require manual intervention with well-trained personnel. Fifth, the measurement and image analysis operations are not suited for high temperature and high pressure conditions.        